arXiv subjects

T. Mendes

Publications and source records attributed to T. Mendes.

At least 19 recordsLinked to original sources

arXiv2016

Impurities near an Antiferromagnetic-Singlet Quantum Critical Point

Heavy fermion systems, and other strongly correlated electron materials, often exhibit a competition between antiferromagnetic (AF) and singlet ground states. Using exact Quantum Monte Carlo (QMC) simulations, we examine the effect of impurities in the vicinity of such AF- singlet quantum critical points, through an appropriately defined impurity susceptibility, $χ_{imp}$. Our key finding is a connection, within a single calculational framework, between AF domains induced on the singlet side of the transition, and the behavior of the nuclear magnetic resonance (NMR) relaxation rate $1/T_1$. We show that local NMR measurements provide a diagnostic for the location of the QCP which agrees remarkably well with the vanishing of the AF order parameter and large values of $χ_{imp}$. We connect our results with experiments on Cd-doped CeCoIn$_5$.

cond-mat.str-el↗

arXiv2008

Efficient use of the Generalized Eigenvalue Problem

We analyze the systematic errors made when using the generalized eigenvalue problem to extract energies and matrix elements in lattice gauge theory. Effective theories such as HQET are also discussed. Numerical results are shown for the extraction of ground-state and excited B-meson masses and the ground-state decay constant in the static approximation.

hep-lat↗

arXiv2007

Constraints on the IR behavior of the gluon propagator in Yang-Mills theories

We present rigorous upper and lower bounds for the zero-momentum gluon propagator D(0) of Yang-Mills theories in terms of the average value of the gluon field. This allows us to perform a controlled extrapolation of lattice data to infinite volume, showing that the infrared limit of the Landau-gauge gluon propagator in SU(2) gauge theory is finite and nonzero in three and in four space-time dimensions. In the two-dimensional case we find D(0) = 0, in agreement with Ref. [1]. We suggest an explanation for these results. We note that our discussion is general, although we only apply our analysis to pure gauge theory in Landau gauge. Simulations have been performed on the IBM supercomputer at the University of Sao Paulo.

hep-lat↗

arXiv2007

Just how different are SU(2) and SU(3) Landau-gauge propagators in the IR regime?

The infrared behavior of gluon and ghost propagators in Yang-Mills theories is of central importance for understanding quark and gluon confinement in QCD. While simulations of pure SU(3) gauge theory correspond to the physical case in the limit of infinite quark mass, the SU(2) case (i.e. pure two-color QCD) is usually employed as a simplification, in the hope that qualitative features be the same as for the SU(3) case. Here we carry out the first comparative study of lattice (Landau) propagators for these two gauge groups. Our data were especially produced with equivalent lattice parameters in order to allow a careful comparison of the two cases. We find very good agreement between SU(2) ans SU(3) propagators, showing that in the IR limit the equivalence of the two cases is quantitative, at least down to about 1 GeV. Our results suggest that the infrared behavior of these propagators is independent of the gauge group SU(N_c), as predicted by Schwinger-Dyson equations.

hep-lat↗

arXiv2007

SU(2) meets SU(3) in lattice-Landau-gauge gluon and ghost propagators

A comparative study of the lattice Landau gauge gluon and ghost propagators for SU(2) and SU(3) pure Yang-Mills theories is carried out. The data were specially produced with equivalent lattice parameters to allow for a careful comparison of the two cases. We find very good agreement between the two theories. Our results seem to confirm the predicton of Schwinger-Dyson equations that the infrared exponents are independent of the gauge group SU(N).

hep-lat↗

arXiv2006

Comparison among HB-inspired algorithms for continuous-spin systems and gauge fields

We propose a new local algorithm for the thermalization of n-vector spin models, which can also be used in the numerical simulation of SU(N) lattice gauge theories. The algorithm combines heat-bath (HB) and micro-canonical updates in a single step -- as opposed to the hybrid overrelaxation method, which alternates between the two kinds of update steps -- while preserving ergodicity. We test our proposed algorithm in the case of the one-dimensional 4-vector spin model and compare its performance with the standard HB algorithm and with other HB-inspired algorithms.

hep-lat↗

arXiv2006

Dynamic Critical Behavior of Percolation Observables in the 2d Ising Model

We present preliminary results of our numerical study of the critical dynamics of percolation observables for the two-dimensional Ising model. We consider the (Monte-Carlo) short-time evolution of the system obtained with a local heat-bath method and with the global Swendsen-Wang algorithm. In both cases, we find qualitatively different dynamic behaviors for the magnetization and Omega, the order parameter of the percolation transition. This may have implications for the recent attempts to describe the dynamics of the QCD phase transition using cluster observables.

hep-lat↗

arXiv2005

Numerical Study of the Ghost-Gluon Vertex in Landau gauge

We present a numerical study of the ghost-gluon vertex and of the corresponding renormalization function \widetilde{Z}_1(p^2) in minimal Landau gauge for SU(2) lattice gauge theory. Data were obtained for three different lattice volumes (V = 4^4, 8^4, 16^4) and for three lattice couplings β= 2.2, 2.3, 2.4. Gribov-copy effects have been analyzed using the so-called smeared gauge fixing. We also consider two different sets of momenta (orbits) in order to check for possible effects due to the breaking of rotational symmetry. The vertex has been evaluated at the asymmetric point (0;p,-p) in momentum-subtraction scheme. We find that \widetilde{Z}_1(p^2) is approximately constant and equal to 1, at least for momenta p > ~ 1 GeV. This constitutes a nonperturbative verification of the so-called nonrenormalization of the Landau ghost-gluon vertex. Finally, we use our data to evaluate the running coupling constant α_s(p^2).

hep-lat↗

arXiv2004

Numerical Study of the Ghost-Ghost-Gluon Vertex on the Lattice

It is well known that, in Landau gauge, the renormalization function of the ghost-ghost-gluon vertex \widetilde{Z}_1(p^2) is finite and constant, at least to all orders of perturbation theory. On the other hand, a direct non-perturbative verification of this result using numerical simulations of lattice QCD is still missing. Here we present a preliminary numerical study of the ghost-ghost-gluon vertex and of its corresponding renormalization function using Monte Carlo simulations in SU(2) lattice Landau gauge. Data were obtained in 4 dimensions for lattice couplings beta = 2.2, 2.3, 2.4 and lattice sides N = 4, 8, 16.

hep-lat↗

arXiv2004

Temporal correlator in YM^2_3 and reflection-positivity violation

We consider numerical data for the lattice Landau gluon propagator obtained at very large lattice volumes in three-dimensional pure SU(2) Yang-Mills gauge theory (YM^2_3). We find that the temporal correlator C(t) shows an oscillatory pattern and is negative for several values of t. This is an explicit violation of reflection positivity and can be related to gluon confinement. We also obtain a good fit for this quantity in the whole time interval using a sum of Stingl-like propagators.

hep-lat↗

arXiv2002

Vortex induced confinement and the IR properties of Green functions

Simulations of SU(2) lattice gauge theory are used to establish a relation between the IR properties of Green functions and confinement. Using Landau gauge where the gauge configurations are restricted to the first Gribov regime, results on the ghost-, gluon form-factor and the running coupling constant are presented. Finally, we discuss the behavior of the ghost form-factor of the de-confined phase at high temperatures.

hep-th↗

arXiv2002

Universal amplitude ratios from numerical studies of the three-dimensional O(2) model

We investigate the three-dimensional O(2) model near the critical point by Monte Carlo simulations and calculate the major universal amplitude ratios of the model. The ratio U_0=A+/A- is determined directly from the specific heat data at zero magnetic field. The data do not, however, allow to extract an accurate estimate for alpha. Instead, we establish a strong correlation of U_0 with the value of alpha used in the fit. This numerical alpha-dependence is given by A+/A- = 1 -4.20(5) alpha + O(alpha^2). For the special alpha-values used in other calculations we find full agreement with the corresponding ratio values, e. g. that of the shuttle experiment with liquid helium. On the critical isochore we obtain the ratio xi+/xi-_T=0.293(9), and on the critical line the ratio xi_T^c/xi_L^c=1.957(10) for the amplitudes of the transverse and longitudinal correlation lengths. These two ratios are independent of the used alpha or nu-values.

cond-mat.stat-mech↗

arXiv2001

Comparison of finite-size-scaling functions for 3d O(N) spin models to QCD

We calculate numerically universal finite-size-scaling functions of the magnetization for the three-dimensional O(4) and O(2) spin models. The approach of these functions to the infinite-volume scaling functions is studied in detail on the critical and pseudocritical lines. For this purpose we determine the pseudocritical line in two different ways. We find that the asymptotic form of the finite-size-scaling functions is already reached at small values of the scaling variable. A comparison with QCD lattice data for two flavours of staggered fermions shows a similar finite-size behaviour which is compatible with that of the spin models.

hep-lat↗

arXiv2001

Finite-size-scaling functions for 3d O(4) and O(2) spin models and QCD

We calculate numerically universal finite-size-scaling functions for the three-dimensional O(4) and O(2) models. The approach of these functions to the infinite-volume scaling functions is studied in detail on the critical and pseudocritical lines. For this purpose we determine the pseudocritical line in two different ways. We find that the asymptotic form of the finite-size-scaling functions is already reached at small values of the scaling variable. A comparison with QCD lattice data for two flavours of staggered fermions shows a similar finite-size behaviour which is compatible with that of the spin models.

hep-lat↗

arXiv2000

A numerical study of Goldstone-mode effects and scaling functions of the three-dimensional O(2) model

We investigate numerically the three-dimensional O(2) model on 8^3-160^3 lattices as a function of the magnetic field H. In the low-temperature phase we verify the H-dependence of the magnetization M induced by the Goldstone modes and determine M in the thermodynamic limit on the coexistence line both by extrapolation and by chiral perturbation theory. We compute two critical amplitudes from the scaling behaviours on the coexistence line and on the critical line. In both cases we find negative corrections to scaling. With additional high temperature data we calculate the scaling function and show that it has a smaller slope than that of the O(4) model. For future tests of QCD lattice data we study as well finite-size-scaling functions.

hep-lat↗

arXiv2000

Cluster Percolation in O(n) Spin Models

The spontaneous symmetry breaking in the Ising model can be equivalently described in terms of percolation of Wolff clusters. In O(n) spin models similar clusters can be built in a general way, and they are currently used to update these systems in Monte Carlo simulations. We show that for 3-dimensional O(2), O(3) and O(4) such clusters are indeed the physical `islands' of the systems, i.e., they percolate at the physical threshold and the percolation exponents are in the universality class of the corresponding model. For O(2) and O(3) the result is proven analytically, for O(4) we derived it by numerical simulations.

hep-lat↗

arXiv2000

Equation of state and Goldstone-mode effects of the three-dimensional O(2) model

We investigate numerically the three-dimensional O(2) model on 8^3-160^3 lattices as a function of the magnetic field H. In the low-temperature phase we verify the H-dependence of the magnetization M induced by Goldstone modes and determine M in the thermodynamic limit both by extrapolation and by chiral perturbation theory. This enables us to calculate the corresponding critical amplitude. At T_c the critical scaling behaviour of the magnetization as a function of H is used to determine another critical amplitude. In both cases we find negative corrections-to-scaling. Our low-temperature results are well described by the perturbative form of the model's magnetic equation of state, with coefficients determined nonperturbatively from our data. The O(2) scaling function for the magnetization is found to have a smaller slope than the one for the O(4) model.

hep-lat↗

arXiv1999

Goldstone-mode effects and scaling function for the three-dimensional O(4) model

We investigate numerically the three-dimensional O(4) model on 24^3-120^3 lattices as a function of the magnetic field H. We verify explicitly the singularities induced by Goldstone modes in the low-temperature phase of the model, and show that they are also observed close to the critical temperature. Our results are well described by the perturbative form of the model's magnetic equation of state, with coefficients determined nonperturbatively from our data. The resulting expression is used to generate the magnetization's scaling function parametrically.

hep-lat↗